固有値問題の解法

固有値は固有方程式(characteristic equation)
det (A − λI) = 0
の解となる。これから，固有方程式を解くことによって固有値を求めることが考えられる。これを直接解法という。行列Aの次元が大きくなると，固有方程式は高次元のλに関する多項式方程式となり，その係数を計算するのに手間がかかる，と同時に，．．．よって，固有方程式を解いて固有値を求めることは通常行われない。

固有値問題を解くには反復解法が普通用いられる。その基礎はシュール(Schur)分解と呼ばれるつぎの事実である ．．．

大石「数値計算講義ノート 6　固有値問題の解法」
 http://www.waseda.jp/ocw/ComputerScience/17-1004345-01NumericalComputationsSpring2003/StudyMaterials/lec6.pdf

http://www.oishi.info.waseda.ac.jp/~oishi/lec2003/num.htm

Elasticity of Substitution for Production Functions

 http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/elasticity%20of%20substitutionrevised.pdf

CES Function and Inada Condition

通常のCES関数は、稲田条件のどちらか一方を満たさない。CES関数で稲田条件と矛盾しない関数はコブ＝ダグラス関数だけである。

國府田「新古典派生産関数の一次同次性と凹性についてのノート」
https://appsv.main.teikyo-u.ac.jp/tosho/kkoda62.pdf

Lyapunov/ Asymptotic Stability

Lyapunov Stability
If all solutions of the dynamical system that start out near an equilibrium point x0 stay near x0 forever, then x0 is Lyapunov stable.

Asymptotic Stability
More strongly, if x0 is Lyapunov stable and all solutions that start out near x0 converge to x0, then x0 is asymptotically stable.

http://en.wikipedia.org/wiki/Lyapunov_stability

限定名詞の代用詞の使い分けthe one (the ones)/ that (those)

限定名詞の代用詞であるthe one (the ones)とthat (those)は、原則的に互換性がある。ただし、以下の点に注意する必要がある。

（１）thatは不加算名詞の代用になるが、the oneはならない

（２）thatは人の代用詞にならないが、thoseはなる

（３）thatはゼロ関係代名詞（＊）節の先行詞にはならない
＊音声形を持たない関係代名詞、いわゆる省略可能な目的格の関係代名詞のこと

（４）thatは形容詞で修飾できない

http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1112523461

http://www.ravco.jp/cat/view.php?cat_id=5588

http://ja.wikipedia.org/wiki/%E9%96%A2%E4%BF%82%E8%A9%9E

it/this/thatの使い分け

前文の内容を表すit/this/thatの使い分け

it: 前文の内容を特別強調しない

this: itに比べ強調効果があり、thatと比べ主観的

that: itに比べ強調効果があり、thisと比べ客観的


http://tottocobkhinata.cocolog-nifty.com/bizieizakkicho/2006/01/it_this_that_3789.html

http://www.ravco.jp/cat/view.php?cat_id=5563

Neutrality/Superneutrality of Money

Neutrality of Money
Any change in the nominal quantity of money that is matched by a proportional change in the price level, leaving m(real balances) unchanged, has no effect on the economy's real equilibrium.

Superneutrality of Money
The steady-state values of the capital stock, consumption, and output (in other words, real variables except real money balances) are all independent of the rate of growth of the nominal money shock.

Walsh, "Monetary Theory and Policy (3rd ed.)" pp.41-43.

Skill-Biased Technical Change

"Skill-Biased Technical Change (SBTC thereafter) is a shift in the production technology that favors skilled (e.g., more educated, more able, more experienced) labor over unskilled labor by increasing its relative productivity and, therefore, its relative demand. Ceteris paribus, SBTC induces a rise in the skill premium—the ratio of skilled to unskilled wages."

Violante, "Skill-Biased Technical Change"
http://www.econ.nyu.edu/user/violante/Books/sbtc_january16.pdf

"アメリカでは1990 年代には賃金格差の要因をめぐって、特にコンピュータ化に代表される技 術革新が高スキル労働者に対する相対需要を増大したことが所得格差をもたらしたというスキ ル偏向型技術進歩（Skill-Biased Technical Change: SBTC）仮説が盛んに唱えられていた。"

池永,"労働市場の二極化 ―ＩＴの導入と業務内容の変化について―"
http://www.jil.go.jp/institute/zassi/backnumber/2009/02-03/pdf/073-090.pdf

Fisher Premium

F≡(1+n)E(p(t)/p(t+1))-(1+r)

n: nominal interest rate
p: price level
r: real interest rate

LeRoy, 1984, "Nominal Prices and Interest Rates in General Equilibrium: Endowment Shocks"

Types of Goods (Normal/Inferior/Luxury/Necessity/Ordinary/Giffen)

Settings
x(p,w): Walrasian demand function of a good
p: Price of the good
w: Wealth (Income)

Normal Goods
∂x/∂w>0

Inferior Goods
∂x/∂w<0

Luxury Goods
(∂x/∂w)(w/x)>1

Necessity Goods
(∂x/∂w)(w/x)<1

Ordinary Goods
(∂x/∂p)<0

Giffen Goods
(∂x/∂p)>0

http://en.wikipedia.org/wiki/Good_%28economics%29

Partial Derivatives of Homogeneous Functions

if a function is homogeneous of degree k, its derivatives are homogeneous of degree k-1.

http://www.economics.utoronto.ca/osborne/MathTutorial/HOMF.HTM

A Principal Reason for Canada-US FTA in 1989

It has long been thought that increasing returns to scale might be an important reason to have trade between countries: if a firm with increasing returns is able to sell in a foreign market, this expansion of output will bring a reduction in its average costs of production, which is an indication of greater efficiency. Indeed, this was a principal reason that Canada entered into a free-trade agreement with the United States in 1989: to give its firms free access to the large American market.

R. Feenstra, 2004, "Advanced International Trade," p.5